You should read the upgrade instructions provided since it varies by OS. But yes you can upgrade directly.
You will need a new 9.7 license, but you will get a 90 day free trial before the new license is installed.
The easiest way is to use the latest fixpack code from the fixpack download site, and then get the 9.7 license-only files from Passport Advantage (I think they are called "Activation", but don't recall for certain). The license is a separate download, or it is automatically included and installed in full 9.7 download. The problem with installing the full 9.7 download is that it is FP 0, and you will have to then download and upgrade to FP 3a.